Experimental and numerical investigations of the generation of resonant sound by flow in a duct containing two sets of baffles and the "feedback" of the sound on the vortex shedding process are reported. The experiments are conducted in a wind tunnel and the numerical simulations are used to predict the sources of resonant sound in the flow. The resonant sound field, which is principally longitudinal, is calculated by the finite element method and a discrete-vortex model is used to predict the observed separated flow. Analysis of the passage of a single point vortex past a baffle indicates that the amount of acoustic energy generated is a function of the phase of the acoustic cycle at which the vortex passes the baffle. A more elaborate model simulates the growth of vortex clouds through the clustering of elemental vortices shed from an upstream baffle, tracks the passage of these vortex clouds past a downstream baffle, predicts the generation of acoustic energy using Howe's theory of aerodynamic sound, and accounts for the feedback of sound on the vortex shedding. Comparison is made between the predicted time-dependent structures and the observed flow structures using smoke visualization. The vortex cloud model predicts the flow conditions under which net acoustic energy is generated by the flow and therefore when resonance can be sustained; the results are consistent with the occurrence of peaks in the observed resonant sound pressure levels.